Dissipative Dynamics of a Quantum System.

The dynamics of a macroscopic degree of freedom is inherently dissipative. Given an accepted model for a dissipative quantum system, a calculational scheme is proposed and is used to calculate the dissipative quantum tunneling rate from a metastable well. The results are estimated to have errors no larger than 0.1% in the exponent and less than 2% in the prefactor. An important theoretical issue in modeling the environment is how the detailed nature of the environment affects the characterization of dissipation. An exact and unified formalism is formulated for a two-stage system coupled to the environment. The formalism is then applied to the case of Ohmic dissipation of harmonic-oscillator heat bath and to the case of fermionic heat bath. The conclusion is that these two cases are very similar, although a crucially important dimensionless parameter (alpha) assumes different range of values in the two different cases. To further our understanding of dissipation in a quantum system, the quantum analogue of the classical Fokker-Planck equation is derived. The major difference between the quantum and the classical Fokker-Planck equations arises from the presence of a quantum mechanical memory term which is non-Markovian and tends to zero in the limit of kT much greater than (omega)(,s), where (omega)(,s) is a characteristic angular frequency of the coupled system.